We went to the market to buy some fruit. We decided to buy some apples, strawberries, and oranges. If we buy 2 apples, 3 boxes of strawberry, and 4 oranges, the fruit would cost $15.30. If we buy 1 box of strawberry, 4 apples, and 2 oranges, the fruit would cost $10.90. If we buy 1 orange, 5 apples and 2 boxes of strawberry, the fruit would cost $13.70. Use the Gaussian Elimination Method to solve for the price of each fruit.

Answers

Answer 1

Step-by-step explanation:

Let the amount of apples bought be x

Amount of strawberries bought be y and;

amount of oranges bought be z

If we buy 2 apples, 3 boxes of strawberry, and 4 oranges, the fruit would cost $15.30, then this will be expressed as;

2x+3y+4z = 15.30 ........... 1

If we buy 1 box of strawberry, 4 apples, and 2 oranges, the fruit would cost $10.90, this will be expressed as:

4x+y+2z = 10.90 ......... 2

If we buy 1 orange, 5 apples and 2 boxes of strawberry, the fruit would cost $13.70, this is expressed as:

5x+2y+x = 13.70 .......... 3

Solving the three equations simultaneously:

2x+3y+4z = 15.30 ........... 1

4x+y+2z = 10.90 ......... 2

5x+2y+z = 13.70 .......... 3

Reduce the number of equations

multiply equation 1 by 2 and subtract from equation 2

equation 1 * 2 will give:

4x+6y+8z = 30.6 ........... 4

eqn (4)-eqn(2)

6y-y + 8z-2z = 30.6-10.90

5y+6z = 19.7 ......... 5

Also multiply equation 2 by 5 and eqn 5 by 4 and subtract from each other.

eqn(2)* 5 will give:

20x+5y+10z = 54.5 .......... *

eqn(3) * 4 will give

20x+8y+4z = 54.8.......**

Subtsrct ** from *

8y-3y+(4z-10z)= 54.8-54.5

5y-6z = 0.3 .................. 6

Equate 5 and 6 and solve:

5y+6z = 19.7 ......... 5

5y-6z = 0.3 .................. 6

subtract:

6z+6z = 19.7+0.3

12z = 20

z = 20/12

z = 1.67

Substitute z = 1.67 into eqn 6

5y-6(1.67) = 0.3

5y - 10 = 0.3

5y = 10.3

y = 10.3/5

y = 2.06

Substitute z = 1.67 and y = 2.06 into equation 1

From 1:

2x+3y+4z = 15.30

2x+3(2.06)+4(1.67) = 15.30

2x+6.18+6.68 = 15.30

2x+12.86 = 15.30

2x = 15.30-12.86

2x = 2.44

x = 2.44/2

x = 1.22

Therefore 1 apple costs $1.22, 1 strawberry costs $2.06 and 1 orange costs $1.67


Related Questions

I have a riddle for you I have 31 82,400,060 tens and 100 hundreds

Answers

Answer: 31824010600

Step-by-step explanation: 3182400060 tens and 100 hundreds = 31824010600.

A ball thrown straight up in the air travels 90 inches in the first tenth of a second. In the next tenth of a second the ball travels 85 inches. After each additional tenth of a second, the ball travels 5 inches less than it did during the preceding tenth of a second. How long will it take before the ball starts coming back down? What is the total distance that the ball has traveled once it reaches its maximum height?

Answers

Answer:

855

Step-by-step explanation:

1.9 seconds is 19 tenths, so that means we add using the information given, which is that the ball travels 5 fewer inches every tenth of a second:

Time | Inches traveled

0.1     | 90

0.2    | 85

0.3    | 80

0.4    | 75

0.5    | 70

0.6    | 65

0.7    | 60

0.8    | 55

0.9    | 50

1.0     | 45

1.1      | 40

1.2     | 35

1.3     | 30

1.4     | 25

1.5     | 20

1.6     | 15

1.7     | 10

1.8     | 5

1.9     | 0

90+85+80+75+70+65+60+55+50+45+40+35+30+25+20+15+10+5+0=855

The lateral surface area of a cube is 400cm². Its total surface area is
_______
a)600cm² b) 2400cm² c) 500cm² d) 650cm²

Answers

Answer:

Step-by-step explanation:

Lateral surface area of cube = 4a²

4a² = 400

   a² = 400÷4

  a² = 100

 a = √100 = √10*10

a = 10 cm

Total surface area = 6a²

                               = 6 * 10²

                               = 6* 100

                               = 600 cm²

Answer:

A

Step-by-step explanation:

I believe that I did this before.

Distribute 3(x^2+2x)

Answers

Answer: 3x^2 +6x

Explanation: Multiply each term in the parentheses by 3.

Answer:3

3[tex]x^{2}[/tex]+6x

is this what you want?

Step-by-step explanation:

Find f(-5) if f(x) = |x + 1|.
A)6
B)5
C)4

Answers

The answer would be C)5

What is equivalent to

Answers

The answer is 3 with a little 7. Alternatively 2187

5=45 ÷
What is the answer

Answers

45 ÷ 5 = 9

So, 5 = 45 ÷ 9

Write 3.19×10−2 in standard form.

Answers

Answer:

It is already in standard form

Please help me answer this question!

Answers

Answer:

D. -3 and 3

Step-by-step explanation:

We are given an output of 2. This means this is the value we need an input for. We need to find a number(s) that lie on the x axis and when we move up, you get an output of 2.

Option A:

If we are given an input of -2, we start at (-2, 0) and move up until we reach a point on the line. We end up lying on the point (-2, 3). Thus, the output for having an input of -2 is 3 which proves that this answer is incorrect.

Option B:

As stated above -2 has an output of 3 which is wrong. Since we know this, we can eliminate this as an option.

Option C:

If we are given an input of -3, we start at (-3, 0) and move up until we reach a point on the line. We end up lying on the point (-3, 2). Thus, the output for having an input of -2 is 2 which proves that this answer is correct.

Option D:

We know that -3 is a possible input so we just need to check 3 as an input.

If we are given an input of 3, we start at (3, 0) and move up until we reach a point on the line. We end up lying on the point (3, 2). Thus, the output for having an input of 3 is 2 which proves that this answer is also correct.

Since we know that -3 and 3 are possible inputs for an output of 2 on the graph, we need to include them both in our answer. Thus, the answer is D.

Best of Luck!

a line in point-slope form that goes through the points (8,-9) and (-4,15).

Answers

Answer: The answer is 1/2

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

Question
Identify the correct graph and solution for the inequality.
10 a <25
(Look at pic)

Answers

i think it is C
explanation:

Answer:

First option

Step-by-step explanation:

First, Solve the inequality:

Divide each side by 10 to cancel out the 10 next to a. It should now look like this: a < 2.5

Find the inequality that matches the solution:

The first option (which literally writes the simplified version of the inequality) is correct, because it matches our simplified inequality above.  

Please help me solve this problem

Answers

Answer:

x=2

Step-by-step explanation:

because if you put the equation as in x+11=6x+1  and do the equation you'll get x=2

Which graph matches the following inequality: y<-2/5x+1?

Answers

Answer: B is the answer

Step-by-step explanation:

5. Ameris rolls a standard number cube with the numbers 1-6. What is the probability of
rolling a 6 or a 2?
a. 16
b. 13
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d. 5%

Answers

Answer: its 2/6 is the answer the choices don't make cense

Step-by-step explanation:

The drama teacher decreased the length of a play from 90 minutes to 60 minutes. What was the percent decrease in the length of the play?

Answers

Answer:

it was decreased by 67%

Step-by-step explanation:

Answer:

67 %

Step-by-step explanation:

Bob needs his refrigerator fixed. The repairman will charge Bob a flat fee of $40 plus an additional $15 for each hour he needs to work on it. Write an equation to represent Bob's cost to repair his refrigerator. Use y for the total cost and x for hours.

Answers

Given:

Fixed fee = $40

Additional fee = $15 per hour

To find:

The equation to represent Bob's cost to repair his refrigerator.

Solution:

Let y be the total cost for x hours.

Additional fee for one hour = $15

Additional fee for x hour = $15x

Total cost = Fixed fee + Additional fee

[tex]y=40+15x[/tex]

Therefore, the required equation is [tex]y=40+15x[/tex].

I’ll mark brainliest

Evaluate the following expression for

m= -3
N= 4
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Answers

(4) / (2) + (-3)

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Answers

Answer:

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Jamal needs to dig a ditch 15 yards long.
Jamal digs 7 yards in the morning and
another 3 yards after lunch. How much is left to dig
more of the ditch is left to dig?

Answers

Answer:

5 yards

Step-by-step explanation:

7y+3y=10yards

15yards-10yards=5yards

Use the distributive property to simplify the following expression-(8+b)

Answers

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Multiply each term inside the parentheses by -1.

Doing so, we get -8 -b.

Nick's phone bill is $50 per month plus $0.25 for every text message. If his bill was $108 this month, how many
text messages did he send?

Answers

Answer:

232 text messages

Step-by-step explanation:

108 - 50 = 58

[tex]58 \div .25[/tex]

232 text messages

Yw :)

232 texts
108-50=58
58/.25=232

i need help with this​

Answers

B is the answer ...............

Answer:

answer is A

Step-by-step explanation:

This symbol is called a tilde. In symbolic logic (a field of math  

used a lot in computer sciences) it is used to denote "not." For  

example, ~A means "not A." In some other contexts, it means  

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Answers

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proportional

Step-by-step explanation:

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19.5/3=6.5

26/4=6.5

32.5/5=6.5

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Answers

It is 2 because:
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For the triangle above, find sin B.
a.
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Answers

Answer:

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sin B = 0.923

C

Helen borrowed $8,000 from her grandfather to pay for college. Five years later, she paid him back the $8,000 and an interest of $1,200. What was the annual interest rate?

Answers

Answer:

3%

Step-by-step explanation:

No explanation

What is the slope of the line that contains these points?
Pls help

Answers

Answer:

-1

Step-by-step explanation:

m=y2-y1/x2-x1

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hope this helps :3

if it did pls mark brainliest

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Answers

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What is the temperature displayed on the thermometer?

Answers

Your Answer :

98.6°F (37°C).

Step - By - Step Explanation :

Your normal body temperature should be around 98.6°F (37°C). If you have a temperature that is over than 100.4°F (37.2°C), then you should see your doctor preferably soon.

Note :

I am sorry if this is the wrong answer to your question. Your query did not have an image to display the temperature on the thermometer nor did your query have any further context for us to examine.

Good luck on your homework and have a great day.

Feel free to comment on my answer if you have any further questions.

Answer:

25

Step-by-step explanation:

It's Correct On Edge As Well :P

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